Automatic Geometry Based FE Model Generation for ...

PAMM · Proc. Appl. Math. Mech. 5, 7–10 (2005) / DOI 10.1002/pamm.200510003

Automatic Geometry Based FE Model Generation for Optimization and Robust Design for Passive Safety of Passenger Vehicles Joergen Hilmann∗1 , Michel Paas∗∗1 , and Volker Schindler∗∗∗2 1 2

Ford of Germany, Cologne Technical University, Berlin

In this paper the optimization of large scale vehicle structures is addressed. A process strategy based on Latin Hypercube sampling, genetic algorithm optimization, and sensitivity analysis is discussed. This process was implemented on a dedicated Linux Cluster, utilizing various free and commercially available software tools, including SFE Concept, Perl, Matlab, and Radioss. The viability of the method is demonstrated for a large scale vehicle model in an offset deformable barrier crash test at 64 kph impact velocity. © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1

Introduction

Competitive pressure, in-house standards, regulatory and public domain requirements are driving the development of more efficient and smarter designs with reduced development times and less prototypes. Intensified usage of numerical methods for vehicle engineering is adopted to address these challenges. Current research efforts in the field of vehicle engineering are focussing on proper deployment of numerical optimization techniques, involving parameter, shape or topology optimization [1-8]. It is anticipated that arbitrary geometrical adaptations, and multi disciplinary optimization will gain even more attention in the near future. In this paper a procedure for automated model generation and optimization is discussed, which allows both material and geometrical properties to be defined as design variables. In addition, sensitivity analysis can be conducted.

Fig. 1

Optimization process chain (1a), simplified optimization process chain (1b)

Prerequisite for structural shape and topology optimization is the ability to automatically generate CAE models. A schematic process chain is shown in Fig.1. The left hand side statements list the subsequent tasks for each iteration; the right hand side displays the process flow. In the optimization process several free and commercially available software programs are utilized, including SFE Concept, Perl, Matlab, and Radioss. Key component in the simulation loop is SFE Concept, which is a parametric tool supporting fast geometry modeling for body in whites combined with a powerful auto-meshing functionality [8-9]. The optimization is based on Genetic Algorithms (GA), which are ideally suited to solve problems with solution spaces that are too large to be exhaustively searched. In [1] the structural optimization procedure was deployed for component models, involving changes in geometry, sheet metal thickness, and material grade. The resulting deformation patterns of a crash box application are depicted in Fig.2. If geometry modifications are prohibited due to vehicle program constraints, the geometrical updates as shown in Fig.1a can be bypassed resulting in a simplified process chain, as shown in Fig.1b. In order to enable processing of large scale vehicle models (Fig.3) it was required to implement the software on a dedicated Linux Cluster. ∗

e-mail: [email protected], Phone: +49 221 90 38024, PreProgram & Concepts Engineering, PD Europe e-mail: [email protected], Phone: +49 221 90 37755, Body Engineering, PD Europe ∗∗∗ e-mail: [email protected], Institute of Automotive Engineering ∗∗

© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Minisymposium M2

Fig. 2

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Bumper system deformation at 60ms: initial generation (left) and after 14 generations (right)

Optimization of vehicle model

In order to reduce turn around times the rear half of the vehicle model was substituted by a rigid body(cf Fig.3). Furthermore, beam elements were introduced in order to obtain well defined force deflection curves representing the doors [9]. A major benefit of this modeling technique is that new program assumptions (e.g. different door load levels) can be incorporated straightforwardly. It is noted that simplified modeling requires verification of similarity in model response. The model is subjected to EuroNCAP test conditions, i.e. an offset deformable barrier impact at 64kph impact velocity. The solution strategy is demonstrated for the following objectives: minimal weight and pulse index, which provides an estimate of occupant chest acceleration based on a simple 1D mass-spring model subjected to the current finite element model acceleration, whilst complying with toe board intrusion constraints. The design variables selected to meet the targets are displayed in Fig.3. The process consist of the following steps:

Fig. 3

2.1

Large scale Finite Element Model (left) and design variables used (right)

Generation of a Latin Hypercube Sample

To expedite the optimization process, the design space is uniformly sampled to gain system knowledge in terms of response surfaces expressing relationships between the design variables and design objectives. For reliable response surface generation the data should be distributed uniformly, covering the full design space. Considering, however, the huge numerical effort that is required in large scale finite element analysis, the total number of runs should be kept to the bare minimum. When the random sample size is limited, Latin Hypercube sampling is ideally suited, since it is guaranteed to generate samples that are relatively uniformly distributed. The best results of the finite element runs based on LH sampling will be used as members in the initial population of the GA optimization. The dots in Fig.4 display normalized intrusions versus weight based on LH sampling. The dark grey dots denote the members of the initial population. It can be easily seen that the initial members already represent solutions in the vicinity of the intrusion targets. Fig.5 displays the linear correlation coefficients of the design variables to the selected objectives. 2.2

Optimization

Genetic algorithms are stochastic iterative search methods that mimic natural biological evolution [10]. GAs operate on a population of potential solutions applying the principle of survival of the fittest to obtain best solutions. For each generation © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

PAMM · Proc. Appl. Math. Mech. 5 (2005)

Fig. 4

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Normalized intrusion vs. normalized weight

its members, representing solutions in the search space, are encoded and evaluated according to its fitness. GAs work in many situations because solutions with above-average fitness receive exponentially increasing trials in subsequent generations. Key parameters of GA involve crossover probability, mutation probability, and population size. Crossover probability denotes how often crossover will be performed. Mutation probability denotes how often parts of chromosomes will be mutated. Population size denotes how many chromosomes are in each population. Major advantages of GAs are:

Fig. 5

Correlation coefficients of 3 design objectives

• Suited for problems with solution spaces that are too large to be extensively searched • Capable of dealing with large sets of design variables, including discrete variables, such as sheet metal thickness • Ideally suited to implementation on parallel computers • GAs can lead to solutions that would otherwise not be considered. Large scale finite element models restrict the maximum number of members per generation. In this example each generation comprises 12 members. The fitness function has been formulated, such that the intrusion constraint is fulfilled prior the weight and pulse index objectives. The light gray dots in Fig.4 show the best members after 5 generations. It can be observed that all solutions have less intrusion than the baseline model. In addition, most members have achieved a significant weight reduction; the best solution managed to achieve a 12% weight reduction compared to the baseline model in conjunction with improved occupant performance as indicated by the pulse index. 2.3

Design Verification

The robustness of the optimized design for perturbations in the sheet thickness was assessed. A random distribution of the sheet thickness around the optimized sheet thickness was established. The range of the distribution was confined by manufacturing constraints. As shown in Fig.6, sheet metal thickness perturbations yield small variations in intrusions. Hence, the optimal design is robust with respect to sheet metal thickness variations induced by steel material specifications. It is noted that perturbations may also occur in other system parameters, e.g. forming effects causing variations in yield behavior.

3

Discussion

A process strategy based on Latin Hypercube, genetic algorithm optimization, and sensitivity analysis was discussed. The viability of the method was demonstrated for a large scale vehicle model was demonstrated and resulted in a significant © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Minisymposium M2

Fig. 6

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System Robustness, Design objective intrusion influenced by sheet metal thickness variations

weight reduction in conjunction with improved occupant performance. In future work robustness analyses with respect to noise factors including yield behavior or test variability (e.g. impact angle, or ride height) will be addressed. Incorporating geometry updates in large scale modeling will provide even more opportunities for design improvement. A further challenge is the parallel optimization for multiple impact modes, which will help overcome traditional trade off conflicts, such as those observed between high and low speed impacts.

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© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim